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Capability with Small Samples

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  • #51599

    Savage
    Participant

    I have a question about conducting a capability study on a small number of parts.  I   manufacture cylinders that go through a broaching process to cut several grooves into the I.D.  The cylinders are very expensive and I currently only have 5 parts.
     
    We measure the depth of the groove at 5 different lengths along the cylinder ( 75mm, 150mm, etc) and at 0, 120, 240 degrees around the cylinder.  So each cylinder has 15 depth measurements.
     
    I’m trying to look at the capability of this process, but I’m not sure I can use the data I have.  Can I use the 75 data points for each cylinder to calculate the capability?  I don’t have logical subgroups like a “textbook” capability study i.e. 20 subgroups of 3-5 measurements.
     
    I’ve looked through numerous references and can’t seem to find anything similar to this.  I’m happy to research more if someone can point me in the right direction.
     
    Go Vikings.
     
    Thanks
     
     

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    #179245

    newbie
    Participant

    Have you already addressed the accuracy and precision of your measurement system and determined stability and distribution type?

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    #179246

    newbie
    Participant

    Once you validate the measurement system, I believe your next step is to determine the stability of your process prior to the capability study.  This requires that you preserved the time order of your data collection.  If you have then you should be able to develop a subgrouping strategy that makes sense (ie minimizes the within subgroup” variation) using 75 observations. 
    I am not aware of any hard and fast rules for determining subgroup size or frequency, although with continuous data and your limited data set, I would think n=3 and k=25 would be appropriate with an XbarR Chart.  
    If stable, you can conduct your capability study based on distribution type and specification characteristics. 
    75 continuous measures are sufficient to hang your statistical hat on I believe, and if reporting short-term capability, I believe it should work as your initial baseline measure. 
    But double-check this info.  Best of luck.

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    #179247

    Anonymous
    Guest

    You should use a Shewhart chart to try and find sources of variation. This means in practice plotting charts in a variety of ways. Years ago when we had no software this was tedious so we used Multi-vari charts to find sources of variation.My advice therefore is to first use what you have and try to find all the sources of variation.You should also be aware that Minitab used Anova which assumes independence. If your data is not independent – which you can check using a scatter diagram, then you can use a graphical method to estimate the contribution of each souce.Typically, you will have machine to machine, and along the tube ( tag the ends if you can.)Remember, if you want to check temporal stability you would need to form subgroups where each sample within a subgroup is collected in the order of manufacture. Don’t use random samples taken out of a Bin.Cheers,
    Andy

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    #179258

    Savage
    Participant

    Thanks Andy/newbie,
    We did have issues with the measurement device initially, but we resolved those problems and moved forward with the study.
    I have already looked at the data on a multi-vari and within piece variation is greatest. 
    My heartburn is in creating subgroups after the data has already been collected.  I have a list of 75 data points.  I don’t have data that was collected as 25 subgroups of n=3.  The best I might be able to use is the subgroups of the angular measurements, so I have 15 subgroups of n=5.  Something doesn’t feel right, but it might just be my lack of confidence. 
    Thanks again.
    Matt

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    #179260

    Anonymous
    Guest

    Hi Matt,If you know the largest source of variation, you’re in an excellent position to do something about it. (This is a common feature with semiconductor furnaces.)Have you tagged your components so you know which way up they went through your machining processes? Sometimes it is possible to reverse orientation in one of the process steps so that the form cancels out the opposing form in a later step.If you can’t do this then you might have to try and understand some machining effects.For example, in a process for grinding image setter drums, there can be differences between the front and the back ID of the drum – two hemi-cylindrical drums pinned together to form a cylindrical drum.If your in a similar situation you might want to check your jig and fixings for flexing under resistance.As for capability, I can’t comment any further as I don’t understand your circumstances. But I personally always try to distinguish the process mean from the process uniformity. By uniformity, I mean the variation within piece. In fact, I ofte prefer to plot the process mean and the process uniformity on separate Shewhart X-bar and R charts.A common mistake and one that set Motorola back many years was to regard sample measurements taken within a piece as a subgroup for temporal variation. Don’t make the same mistake.If you take three measurements within a piece, the average of the three measurements is only one member of the set of n in a Shewhart Chart. In other words, you would need 9 measurements for n = 3 because n is made up of three averages of within piece.I hope this is clear …Good luck,
    Andy

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